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An interactive fractal explorer comparing the CCF Set (Eₙ₊₁ = Eₙ² + Eₙ₋₁) with the CCF Null Cone Set (Eₙ₊₁ = Eₙ² − Eₙ₋₁). Both use the same recurrence with one difference: the sign of the memory term. The CCF Set (β=+1) produces focused directional rays — the Light-Matter Recurrence, modeling χ² nonlinearity with cavity feedback. The CCF Null Cone Set (β=−1) produces divergent explosive rays — the Light-Space Recurrence, corresponding to the spatial discretization of Maxwell’s wave equation in a χ² medium. Testing all values of β from −2 to +2 confirms that only β=±1 produce ray geometry. The sign determines whether light is captured (positive, cavity, focused beam) or free (negative, open space, expansion). Both fractals exhibit 6-fold angular structure from the phase-doubling property of E². Built in vanilla JavaScript with Canvas 2D rendering, pixel-level iteration, scroll/pinch zoom, and drag panning. Part of the Captain Cookie Face Universe (CCFU) — Theory #23.
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Title CCF Set with Null Cone — Light-Matter and Light-Space Recurrences
An interactive fractal explorer comparing the CCF Set (Eₙ₊₁ = Eₙ² + Eₙ₋₁) with the CCF Null Cone Set (Eₙ₊₁ = Eₙ² − Eₙ₋₁). Both use the same recurrence with one difference: the sign of the memory term. The CCF Set (β=+1) produces focused directional rays — the Light-Matter Recurrence, modeling χ² nonlinearity with cavity feedback. The CCF Null Cone Set (β=−1) produces divergent explosive rays — the Light-Space Recurrence, corresponding to the spatial discretization of Maxwell’s wave equation in a χ² medium. Testing all values of β from −2 to +2 confirms that only β=±1 produce ray geometry. The sign determines whether light is captured (positive, cavity, focused beam) or free (negative, open space, expansion). Both fractals exhibit 6-fold angular structure from the phase-doubling property of E². Built in vanilla JavaScript with Canvas 2D rendering, pixel-level iteration, scroll/pinch zoom, and drag panning. Part of the Captain Cookie Face Universe (CCFU) — Theory #23.
Work type Script
Tags ccf simulator, light-matter, captain cookie face, light-space
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Registry info in Safe Creative
Identifier 2604275414333
Entry date Apr 27, 2026, 12:10 PM UTC
License All rights reserved
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Author 100.00 %. Holder Captain Cookie Face Universe. Date Apr 27, 2026.
Information available at https://www.safecreative.org/work/2604275414333-ccf-set-with-null-cone-light-matter-and-light-space-recurrences
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